Leibniz MMS Days 2017 - Abstract
Split-explicit methods are a common integration method in numerical weather prediction. They combine two explicit methods to integrate different parts of the right hand side with different time steps. Common combinations are for the slow part Leap-Frog, Runge-Kutta, or Adams-method and for the fast part a Verlet-type integration method. For Runge-Kutta methods as the slow integrator Wensch et.al give a generalization (MIS-method) and analysed this new method in case of an exact integration of the fast part. When the orography is represented by a cut cell approach the splitting has to respect also the small cell problem. Modifications are described, which represent the fast part by a local linear operator and use a special implicit-explicit method for the integration of this linear differential equation. We will compare our new integrators and known methods for the two-dimensional compressible Euler-equations for examples with different Mach-numbers and grid configurations.